The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1  1  1  1  1  1  X  1  1  1  1  1 3X  1 6X  1  1  1  1  1 3X
 0  1  1  3 5X+2  0  X  X  6 2X  6 X+6 X+6 6X+6 3X+6 2X 5X+4  5 3X+6 5X+1  5  3 5X+2 5X+4  1 X+3 X+5 5X+1  1 4X+2 4X+4 X+3 6X+1 4X+2 4X+4 X+5  1 6X+1 4X+3 X+2 2X+4 3X+5  1 3X+1  1 4X+3 X+2  4 5X+5 3X+1  1
 0  0 5X 3X 6X  X 2X 4X  X 6X 5X 4X 2X 3X  0 5X 4X 6X 6X 3X  0 4X 3X 2X 2X  X 2X  0 4X 4X 3X 2X  X  0 5X 3X 5X 2X  0  X 6X 5X 6X 4X  X 5X 2X  X 4X 6X 3X

generates a code of length 51 over Z7[X]/(X^2) who´s minimum homogenous weight is 298.

Homogenous weight enumerator: w(x)=1x^0+3150x^298+2646x^299+108x^301+2520x^305+882x^306+198x^308+4620x^312+2646x^313+30x^315+6x^336

The gray image is a linear code over GF(7) with n=357, k=5 and d=298.
This code was found by Heurico 1.16 in 0.124 seconds.